The endpoint theorem This paper is dedicated to the memory of Christopher J S Clarke

The endpoint theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It plays a fundamental role in the theory of the abstract boundary...

Full description

Saved in:
Bibliographic Details
Published in:Classical and quantum gravity 2021-02, Vol.38 (6)
Main Authors: Scott, Susan M, Whale, Ben E
Format: Article
Language:English
Subjects:
abstract boundary
accumulation point
embedding
endpoint
envelopment
sequence
singularity theorems
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The endpoint theorem links the existence of a sequence (curve), without accumulation points, in a manifold to the existence of an open embedding of that manifold so that the image of the given sequence (curve) has a unique endpoint. It plays a fundamental role in the theory of the abstract boundary as it implies that there is always an abstract boundary point to represent the endpoint of such sequences and curves. The endpoint theorem will be of interest to researchers analysing specific spacetimes as it shows how to construct a chart in the original manifold which contains the sequence (curve). In particular, it has application to the study of singularities predicted by the singularity theorems.
ISSN:0264-9381
1361-6382
DOI:10.1088/1361-6382/abe1fe